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Can two numbers have $15$ as their HCF and $175$ as their LCM? Give reasons.
Given: Two numbers.
To do: To find weather two numbers have $15$ as their HCF and $175$ as their LCM. and to explain reasons.
Solution:
For 2 or more numbers,
LCM$=$Product of highest power of each factor involved in the numbers.
HCF$=$Product of smallest power of each common factor.
We can conclude that LCM is always a multiple of HCF, i.e.,
LCM$=$ k$\times$ HCF
We are given that
LCM $= 175$
HCF $= 15$
But in this case, LCM $\
eq k\times$ HCF.
eq k\times$ HCF.
Therefore, 2 numbers can't have LCM as $175$ and HCF as $15$.
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